Systems of Equations Graph

Front

What is a system of equations?

Back

A set of two or more equations with the same variables. The solution is the point(s) where the graphs of the equations intersect.

Front

What does it mean for a system of equations to have a unique solution?

Back

It means there is exactly one point where the graphs of the equations intersect.

Front

What does it mean for a system of equations to have no solution?

Back

It means the graphs of the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

How do you graph a linear equation?

Back

You can graph a linear equation by finding two or more points that satisfy the equation and connecting them with a straight line.

Front

What is the substitution method in solving systems of equations?

Back

A method where you solve one equation for one variable and substitute that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What is the point of intersection in a system of equations?

Back

The point where the graphs of the equations meet, representing the solution to the system.

Front

How can you determine if a system of equations has no solution graphically?

Back

If the lines are parallel and do not intersect, the system has no solution.

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

(1, 3)